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Vilka [71]
4 years ago
9

Please answer asap if u know the answer!!!! completing a square. thank you!!!!

Mathematics
1 answer:
Tema [17]4 years ago
3 0

Answer:

D

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form using the method of completing the square.

Given

f(x) = 3x² - 24x + 10

We require the coefficient of the x² term to be 1 , thus factor out 3

3(x² - 8x) + 10

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

= 3(x² + 2(- 4)x + 16 - 16) + 10

= 3(x - 4)² + (3 × - 16) + 10

= 3(x - 4)² - 48 + 10

= 3(x - 4)² - 38, thus

f(x) = 3(x - 4)² - 38 ← in vertex form

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The table shows the different types of shoes available at a family shoe store.
Wittaler [7]

Answer:

about 48.6%

Step-by-step explanation:

20 women's shoes are athletic.

35 women's shoes are formal.

52 women's shoes are casual.

The total number of women's shoes is 107.  So the probability that a randomly selected one is casual is:

P = 52/107

P ≈ 48.6%

6 0
3 years ago
What is the slope of the line on the graph?<br><br><br><br> Enter your answer in the box.
alexira [117]
To find the slope,we can use the slope formula:
\frac{y1 - y2}{x1 - x2}
Where x and y are y coordinates and x coordinates respectively.

To find the answer, put any two points into the formula.

In this case, (1,5) and (0,-1) will be used:

x1 and y1 would be the x and y coordinate in the first point(1,5), while x2 and y2 would be the x and y coordinate in the first point (0,-1)

\frac{5 - ( - 1)}{ 1- 0}  \\  =  \frac{5 + 1}{1}  \\   = \frac{ 6}{1}  \\  = 6
Therefore the answer is 6.

Hope it helps!
5 0
4 years ago
What is <br> 13r+5r <br><br> simplified
sergejj [24]

Answer:

18r

Step-by-step explanation:

since they both have r as their variable, they're like terms, meaning you can combine them

so 13+5 = 18

3 0
3 years ago
The length of a rectangle is 4 m longer than its width. if the perimeter of the rectangle is 36 m , find its area.
ycow [4]
Answer:   The area of the rectangle is:  " 77 m² " .

__________________________________________________________
Note:  The formula for the area, "A" of a rectangle:

 →  A  =  L  *  w   ;

                 in which:  
     A = "area (of rectangle)" ; [in units of "m² " ; that is:  "square meters" ] ; 
                                     
     L = length = "(4 + w)" {in units of "meters (m)" } ;  
             
     w = width  {in units of "meters (m)" } ; 
_______________________________________________________

So;  " A = L * w " ;  

Substitute the known expression for the "length, L" ;  & rewrite the formula for the given area of OUR area for the rectangle in OUR GIVEN PROBLEM:

              →  A = (4 + w) * w '' ;
______________________________________________________

Note the formula for the perimeter, "P" ; 

 →  P = 2L + 2w  ; 

↔   2L + 2w = P 

 →  2L + 2w  = 36 m ;
_____________________________________________________
We want to find the "area" , "A" :
_____________________________________________________
Using the formula for the "perimeter, "P" (of the rectangle) ; & given that the perimeter is:  "36" (meters) ;  

 →  2L + 2w  = 36 ;

 →  Let us plug in the values for "Length (L)" & "width (w)" ; 

 →  2(w + 4)  + 2w = 36  ; 

So;   (2*w) + (2*4) + 2w = 36 ;  Solve for "w" ;

    →  2w + 8 + 2w = 36 ; 

    → Combine the "like terms" :

         + 2w + 2w = 4w ; 

   →  And rewrite: 

         4w + 8 = 36 ; 

Now, subtract "8" from EACH SIDE of the equation:

         4w + 8 − 8 = 36 <span>− 8 ; 
</span>
to get: 

         4w = 28 ; 

Now, divide EACH SIDE of the equation by "4" ; 
      to isolate "w" on EACH SIDE of the equation ; & to solve for "w" ; 

         4w / 4 = 28 / 4  ; 

           → w = 7 ;   → The "width" of the rectangle is:  " 7 m " .

Now, we can find the "length" of the rectangle:

The length, "L" , of the rectangle = 4 + w = 4 + 7 = 11 .
      
           →  L = 11 .  →  The "length" of the rectangle is:  " 11 m " .
___________________________________________________
 
Now, we can find the area, "A", of the rectangle.

 A = L * w  =  11 m * 7 m  =  " 77 m² " .

  →  The area of the rectangle is:  " 77 m² <span>" .
</span>__________________________________________________

To check our answer:
__________________________________________________
 
→  " P = 2L + 2w "  ; 

Given that "P = 36 m" ; 

Plug in "36 m" (for "P") ; into the equation ;

and plug in our calculated values for
                        "length, L" (which is "11 m") ; & "width, w" (which is "7 m") ; 

to see if the equation holds true ; that is, to see if both sides of the equation are equal ;
_______________________________________________________  

 →  36 m = ?  2L + 2w ?? ;

 →  36 m = ?  2(11 m) + 2(7 m) ?? ; 

 →  36 m = ?  22 m + 14 m ?? ; 

 →  36 m = ?  36 m ?  Yes! 
__________________________________________________
3 0
3 years ago
15 percent of what number is 12
blagie [28]
12÷15<u /><em />=160
you have to divide 12 by 15 percent to get the missing number  
5 0
3 years ago
Read 2 more answers
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